I will try to give a rough idea about wave particle duality to people who do not know what it is. All you need to know is what a function is.
What do we mean by a particle? We have this picture of a small ball-like thing, or a point with some mass – that’s somewhere or the other all the time. That’s the defining thing about particles – they have a position at all times. So we can describe a particle’s position by a continuous function x(t). That’s the partcle picture. But for real life objects, can we desribe them that way? Does such a function exist at all times? How do we know?
Now we can’t tell what the position of anything is without looking at it. This ‘looking at it’ is called measurement. So, when we do a position measurement we get a position. But what about before the measurement? There is no way of knowing what x was, or even if there was a position at all. Simply put, we can’t describe the position by x(t) at all times.
Then what is the right way of dealing with real life objects, like electrons and all? That forms the substance of Quantum Mechanics. QM says that, between measurements, all we can say about a variable like position is to give a function f(x,t), called the position wave function. What is the significance of the wave function? If you square it, it gives the probability. So the values of f(x,t)-square at various points will be the probabilities of the position being found there.
How does the wave come in? The wave function of an object varies with space and time in a particular way, but that depends on the surroundings it finds itself in. There’s an equation that describes this variation. If we know the surroundings the object is in, we can find out how the wave function will vary. Under certain circumstances it varies like a wave.
What does that mean? Imagine a wave. It moves along with its crests and troughs, now rising now falling. That’s the same thing that happens to this function. If you graph f(x) with x for a certain time, you will see crests and troughs, and these crests and troughs move forward with time, just like waves do. That’s roughly the idea.
As the wave function varies like a wave, the probability of finding the electron gets to places where only a wave could reach, and particles couldn’t. There’s this phenomenon called interference, shown by waves.
Suppose there are two sources of some kind of wave, placed some distance apart. They flow in crests and troughs. Now suppose they meet at a point where they both have crests. So the two crests will add and make a bigger crest. But suppose a crest meets a equal trough. Then they get cancelled and you get neither crest nor trough. If you take a cardboard with two holes in it, place it before some wall and throw light on ir you will see: Alternate patches of light and darkness on the wall. The two holes act like two sources, sending in the light waves. You get Light where crests meet, dark where crest meets trough.
Now do it with electrons? What do you get, You get the same pattern. Some places on the wall the electrons will hit, at someplaces no electrons will it.. That’s because the wave function is like a wave, it shows interference. It has its crests and troughs. If electrons were particles, we would not get this pattern.
So electrons behave in their own way, which is neither particle nor wave.
( I may restructure and edit this post a bit. Meanwhile, any comments regarding inaccuracies or unclearness of presentation will be particularly welcome)
